Ultimately you want the court to force the party that has grieved you to change and correct the wrong. The court if it rules in your favour is effectively 'threatening' the other party to make it right. They're telling someone to pay the money owed or in some cases they're telling an entity...a business, a city government or department to change their policy or face the wrath of the court.
How does this happen? It starts with papers delivered in the mail. That seems harmless enough, but the seal of the court attached to the document contains a threat. If you don't obey, then men with badges and guns will show up and take it to the next level. They may physically remove you from the building, restrict your movements/take away your freedom to move and/or seize items.
A lawsuit is calling upon a branch of the government to use the threat of violence to modify or remedy a situation.
If we believe in non-resistance and refuse to use violence (as per Romans 12) to order and manage our affairs, it follows that the courts are not really an option for Christians. If I am to turn the other cheek and bless those who persecute me, then I can't say that I'm following that mandate when I call on the agents of Babylon to bear the sword for my purposes.
As I've said before Romans 13 must be understood in light of Romans 12. We've separated them by chapter division but Paul is contrasting the believer with the world and explaining how we are to interact with it. The government is there, serves a Providential purpose but he's basically saying it's 'other'... it's not part of who we are or what we are about.
The magistrates serve their purpose in a generalised sense, but I cannot see that employing them is a viable option for Christians. I think Paul's prohibition in 1 Corinthians 6 extends beyond the mere life of the Church.
Ironically, Church history is riddled with attempts to circumvent this teaching of non-violence and a host of concepts and terms have been invented in order to do so, but they all ultimately deny the contrast Paul is drawing. We are not to be conformed to this world. Being renewed we are able to judge what is right and good and out of that flows a life of self-denial, putting others first, and refusing the world's Lamech-like ethic of violence, pride and revenge. The arguments for Office, Vocation and Just War are all logically structured, but in fact are built on worldly values and philosophy and if they rest on Scripture at all, they rely on faulty hermeneutics.
Practically speaking this presents a real problem for us, especially in the American context. That is, if we are trying to participate in the American system.
In our system the way you challenge the law is to force judicial review. Our democracy has always frowned on the disorder associated with public protest. The way you change the law is to work within the system. The lawsuit forces the issue and if you're right or rather if you can get a good and clever lawyer to make the case, (pardon my cynicism) you can get a law changed or enforced as you desire.
This has proven disastrous as it has opened the floodgates of litigation, and has empowered lawyers and the entire legal profession. This has effectively empowered money... as in, those that have the most, have a better shot in the courts.
In Europe, especially continental Europe, it's not so much the courts as it is grass roots democracy. If you don't like the law, you take to the streets. You demonstrate and you strike. If the discontent is widespread enough, you can organize a general strike.
Of course as Christians this is also problematic. I'm not sure we're to take to the streets, disrupt the civil peace, challenge the police and certainly we're not to engage in violent or destructive behaviour.
Democracy is in general highly problematic. It's dubious on a moral level and in terms of how it functions it can also be both delicate and difficult.
That said, as Christians we probably have a better shot at living in civil peace under a democratic system than some of the alternatives.
But no matter what kind of democracy... or government for that matter, there still is the threat of violence. That's how it works. It's one threat countering another. That's really what checks and balances are all about.
We can be thankful for this form of government but in many ways can't have much to do with it.
The same issues arise when we look at labour unions. We can see why they would arise. We can understand the impulse that leads to their formation. But remember, the threat of the strike which is the 'teeth' of the union... is in the end a threat of violence. We will forcibly ruin your business and physically block your profits. We will sabotage you if we don't get our way.
This in no way alleviates the guilt on the part of many employers who through deceit withhold rightful wages, who manipulate and take advantage of their employees and communities and seek undue gain. Holding people captive through implied threat can also be a form of violence.
We might say that it is good (or not) for society to have strong labour unions, even though we probably can't be part of one. Regardless of our answer it would seem that it's a fight that's not for us.
I contend the more we grasp the issues of society and peel back the veneer and look at them exposed and in their essence, the words of Paul carry great weight. There's a reason we're not to entangle ourselves in the affairs of this life. There's a reason why being a soldier of Christ entails 'dis-entanglement' from the world. There's a reason why we work with our hands and lead quiet lives and pray for peace. It's not because we're invested in the social order. We're not. It's because we have other tasks, other business. We simply want to go about it without any unnecessary hindrances and grief.
And I also contend that only by being outside can we maintain our prophetic witness, integrity and clear vision.